Physical Sciences and Mathematics Commons^™

The Dose-Response Effect Of Aerobic Exercise On Inflammation In Colon Cancer Survivors, Justin C. Brown, Stephanie L.E. Compton, Jeffrey A. Meyerhardt, Guillaume Spielmann, Shengping Yang

School of Medicine Faculty Publications

Background; Physical activity after surgical resection for colon cancer is associated with significantly longer disease-free survival. Inflammation is hypothesized to mediate the association between physical activity and disease-free survival in colon cancer. Methods; In this exploratory analysis of a randomized dose-response trial, 39 colon cancer survivors who completed standard therapy were stratified by cancer stage and randomized in a 1;1;1 ratio to one of three treatment groups for 24 weeks of usual-care control, 150 min/wk of moderate-intensity aerobic exercise (low-dose), or 300 min/wk of moderate-intensity aerobic exercise (high-dose). Inflammation outcomes included high-sensitivity C-reactive protein (hs-CRP), interleukin-6 (IL6), and soluble tumor …

Climate Change Impact On Bridge Scour Risk In Ny State: A Gis-Based Risk Analysis Model, Muhammad Hassan Butt

Publications and Research

Bridge scour, the primary cause of bridge failure in the United States, escalates post-severe storms, necessitating effective mitigation. This study employs a GIS-based risk analysis model to assess climate change's impact on bridge scour and associated risks in New York State. Data from the National Bridge Inventory, climate hazard maps, and geospatial data are integrated.

Is The Declining Birthrate Really An Issue For The Economy?, Harsh Ramesh Pednekar, Theodore Lee, Darrion Chin

Introduction to Research Methods RSCH 202

This study aims to explore the complex implications of declining birth rates on the economy, focusing on GDP per capita as a crucial metric, and aims to uncover both potential opportunities and challenges stemming from this demographic transformation using regression analysis. Using a quantitative methodology and secondary data from OECD.stat, World Population Review, and World Bank, the study explores the relationship between declining birth rates and economic impacts. GDP per capita serves as an essential dependent variable, and it accounts for control variables such as labour force participation, literacy, and education levels, child dependence ratio, and physical capital. Past studies …

The Impact Of Neighborhood Socioeconomic Disadvantage On Operative Outcomes After Single-Level Lumbar Fusion, Grace Y. Ng, Ritesh Karsalia, Ryan S. Gallagher, Austin J. Borja, Jianbo Na, Scott Mcclintock, Neil R. Malhotra

Mathematics Faculty Publications

INTRODUCTION: The relationship between socioeconomic status and neurosurgical outcomes has been investigated with respect to insurance status or median household income, but few studies have considered more comprehensive measures of socioeconomic status. This study examines the relationship between Area Deprivation Index (ADI), a comprehensive measure of neighborhood socioeconomic disadvantage, and short-term postoperative outcomes after lumbar fusion surgery. METHODS: 1861 adult patients undergoing single-level, posterior-only lumbar fusion at a single, multihospital academic medical center were retrospectively enrolled. An ADI matching protocol was used to identify each patient's 9-digit zip code and the zip code-associated ADI data. Primary outcomes included 30- and …

Models Of Shared Care For The Management Of Psychotic Disorder After First Diagnosis In Ontario., Joshua C. Wiener, Rebecca Rodrigues, Jennifer N S Reid, Kelly K. Anderson

Epidemiology and Biostatistics Publications

OBJECTIVE: To describe the provision of care for young people following first diagnosis of psychotic disorder.

DESIGN: Retrospective cohort study using health administrative data.

SETTING: Ontario.

PARTICIPANTS: People aged 14 to 35 years with a first diagnosis of nonaffective psychotic disorder in Ontario between 2005 and 2015 (N=39,449).

MAIN OUTCOME MEASURES: Models of care, defined by psychosis-related service contacts with primary care physicians and psychiatrists during the 2 years after first diagnosis of psychotic disorder.

RESULTS: During the 2-year follow-up period, 29% of the cohort received only primary care, 30% received only psychiatric care, and 32% received both primary and …

Good Practices And Common Pitfalls In Climate Time Series Changepoint Techniques: A Review, Robert B. Lund, Claudie Beaulieu, Rebecca Killick, Qiqi Lu, Xueheng Shi

Department of Statistics: Faculty Publications

Climate changepoint (homogenization) methods abound today, with a myriad of techniques existing in both the climate and statistics literature. Unfortunately, the appropriate changepoint technique to use remains unclear to many. Further complicating issues, changepoint conclusions are not robust to perturbations in assumptions; for example, allowing for a trend or correlation in the series can drastically change changepoint conclusions. This paper is a review of the topic, with an emphasis on illuminating the models and techniques that allow the scientist to make reliable conclusions. Pitfalls to avoid are demonstrated via actual applications. The discourse begins by narrating the salient statistical features …

Access To A Regular Primary Care Physician Among Young People With Early Psychosis In Ontario, Canada, Rebecca Rodrigues, Jennifer N S Reid, Joshua C. Wiener, Suzanne Archie, Richard G Booth, Chiachen Cheng, Arlene G Macdougall, Lena Palaniyappan, Bridget L Ryan, Aristotle Voineskos, Paul Kurdyak, Saadia Hameed Jan, Kelly K. Anderson

Epidemiology and Biostatistics Publications

AIM: Access to a primary care physician in early psychosis facilitates help-seeking and engagement with psychiatric treatment. We examined access to a regular primary care physician in people with early psychosis, compared to the general population, and explored factors associated with access.

METHODS: Using linked health administrative data from Ontario (Canada), we identified people aged 14-35 years with a first diagnosis of nonaffective psychotic disorder (n = 39 449; 2005-2015). We matched cases to four randomly selected general population controls based on age, sex, neighbourhood, and index date (n = 157 796). We used modified Poisson regression to estimate prevalence …

Probability Distributions Arising In Connection With The Inspection Paradox For Bernoulli Trials., James E. Marengo, Anne Marino Himes, W. Cade Reinberger, David L. Farnsworth

Articles

In renewal theory, the Inspection Paradox refers to the fact that an interarrival period in a renewal process which contains a fixed inspection time tends to be longer than one for the corresponding uninspected process. We focus on the paradox for Bernoulli trials. Probability distributions and moments for the lengths of the interarrival periods are derived for the inspected process, and we compare them to those for the uninspected case.

Statistical And Machine Learning Approaches To Describe Factors Affecting Preweaning Mortality Of Piglets, Md Towfiqur Rahman, Tami M. Brown-Brandl, Gary A. Rohrer, Sudhendu R. Sharma, Vamsi Manthena, Yeyin Shi

Department of Biological Systems Engineering: Papers and Publications

High preweaning mortality (PWM) rates for piglets are a significant concern for the worldwide pork industries, causing economic loss and well-being issues. This study focused on identifying the factors affecting PWM, overlays, and predicting PWM using historical production data with statistical and machine learning models. Data were collected from 1,982 litters from the United States Meat Animal Research Center, Nebraska, over the years 2016 to 2021. Sows were housed in a farrowing building with three rooms, each with 20 farrowing crates, and taken care of by well-trained animal caretakers. A generalized linear model was used to analyze the various sow, …

Data Sharing And Ontology Use Among Agricultural Genetics, Genomics, And Breeding Databases And Resources Of The Agbiodata Consortium, Jennifer L. Clarke, Laurel D. Cooper, Monica F. Poelchau, Tanya Z. Berardini, Justin Elser, Andrew D. Farmer, Stephen Ficklin, Sunita Kumari, Marie-Angélique Laporte, Rex T. Nelson, Rie Sadohara, Peter Selby, Anne E. Thessen, Brandon Whitehead, Taner Z. Sen

Department of Statistics: Faculty Publications

Over the last couple of decades, there has been a rapid growth in the number and scope of agricultural genetics, genomics and breeding databases and resources. The AgBioData Consortium (https://www.agbiodata.org/) currently represents 44 databases and resources (https://www.agbiodata.org/databases) covering model or crop plant and animal GGB data, ontologies, pathways, genetic variation and breeding platforms (referred to as ‘databases’ throughout). One of the goals of the Consortium is to facilitate FAIR (Findable, Accessible, Interoperable, and Reusable) data management and the integration of datasets which requires data sharing, along with structured vocabularies and/or ontologies. Two AgBioData working groups, focused on Data Sharing and …

Repurposing The Fda-Approved Anthelmintic Pyrvinium Pamoate For Pancreatic Cancer Treatment: Study Protocol For A Phase I Clinical Trial In Early-Stage Pancreatic Ductal Adenocarcinoma, Francesca M. Ponzini, Christopher W. Schultz, Benjamin E. Leiby, Shawnna Cannaday, T. Yeo, James Posey, Wilbur B. Bowne, Charles Yeo, Jonathan R. Brody, Harish Lavu, Avinoam Nevler

Department of Surgery Faculty Papers

BACKGROUND: Recent reports of the utilisation of pyrvinium pamoate (PP), an FDA-approved anti-helminth, have shown that it inhibits pancreatic ductal adenocarcinoma (PDAC) cell growth and proliferation in-vitro and in-vivo in preclinical models. Here, we report about an ongoing phase I open-label, single-arm, dose escalation clinical trial to determine the safety and tolerability of PP in PDAC surgical candidates.

METHODS AND ANALYSIS: In a 3+3 dose design, PP is initiated 3 days prior to surgery. The first three patients will be treated with the initial dose of PP at 5 mg/kg orally for 3 days prior to surgery. Dose doubling will …

A Classical Fall Statistics Problem, Timothy L. Meyer

Cornhusker Economics

An evaluation of traditional baseball measures and suggestions for alternatives, centering on statistics related to the offensive quality of a player.

Multi-Representation Variational Autoencoder Via Iterative Latent Attention And Implicit Differentiation, Nhu Thuat Tran, Hady Wirawan Lauw

Research Collection School Of Computing and Information Systems

Variational Autoencoder (VAE) offers a non-linear probabilistic modeling of user's preferences. While it has achieved remarkable performance at collaborative filtering, it typically samples a single vector for representing user's preferences, which may be insufficient to capture the user's diverse interests. Existing solutions extend VAE to model multiple interests of users by resorting a variant of self-attentive method, i.e., employing prototypes to group items into clusters, each capturing one topic of user's interests. Despite showing improvements, the current design could be more effective since prototypes are randomly initialized and shared across users, resulting in uninformative and non-personalized clusters.To fill the gap, …

Lightning Forecast From Chaotic And Incomplete Time Series Using Wavelet De-Noising And Spatiotemporal Kriging, Jared K. Nystrom, Raymond Hill, Andrew J. Geyer, Joseph J. Pignatiello Jr., Eric Chicken

Faculty Publications

Purpose: Present a method to impute missing data from a chaotic time series, in this case lightning prediction data, and then use that completed dataset to create lightning prediction forecasts.

Design/Methodology/Approach: Using the technique of spatiotemporal kriging to estimate data that is autocorrelated but in space and time. Using the estimated data in an imputation methodology completes a dataset used in lighting prediction.

Findings: The techniques provided prove robust to the chaotic nature of the data, and the resulting time series displays evidence of smoothing while also preserving the signal of interest for lightning prediction.

Abstract © Emerald Publishing …

Sugar-Sweetened Beverages And Artificially Sweetened Beverages Consumption And The Risk Of Nonalcoholic Fatty Liver (Nafld) And Nonalcoholic Steatohepatitis (Nash), Tung Sung Tseng, Wei Ting Lin, Peng Sheng Ting, Chiung Kuei Huang, Po Hung Chen, Gabrielle V. Gonzalez, Hui Yi Lin

School of Public Health Faculty Publications

Nonalcoholic fatty liver disease (NAFLD) and nonalcoholic steatohepatitis (NASH) are fast becoming the most common chronic liver disease and are often preventable with healthy dietary habits and weight management. Sugar-sweetened beverage (SSB) consumption is associated with obesity and NAFLD. However, the impact of different types of SSBs, including artificially sweetened beverages (ASBs), is not clear after controlling for total sugar intake and total caloric intake. The aim of this study was to examine the association between the consumption of different SSBs and the risk of NAFLD and NASH in US adults. The representativeness of 3739 US adults aged ≥20 years …

History And Current Status Of Mediterranean Spotted Fever (Msf) In The Crimean Peninsula And Neighboring Regions Along The Black Sea Coast, Muniver T. Gafarova, Marina E. Eremeeva

Department of Biostatistics, Epidemiology, and Environmental Health Sciences Faculty Publications

Mediterranean spotted fever (MSF) is a tick-borne rickettsiosis caused by Rickettsia conorii subspecies conorii and transmitted to humans by Rhipicephalus sanguineus ticks. The disease was first discovered in Tunisia in 1910 and was subsequently reported from other Mediterranean countries. The first cases of MSF in the former Soviet Union were detected in 1936 on the Crimean Peninsula. This review summarizes the historic information and main features of MSF in that region and contemporary surveillance and control efforts for this rickettsiosis. Current data pertinent to the epidemiology of the disease, circulation of the ticks and distribution of animal hosts are discussed …

The Public Health Impact Of Paxlovid Covid-19 Treatment In The United States, Yuan Bai, Zhanwei Du, Lin Wang, Eric H. Y. Lau, Isaac Fung, Petter Holme, Ben Cowling, Alison Galvani, Robert Krug, Lauren Ancel Meyers

Department of Biostatistics, Epidemiology, and Environmental Health Sciences Faculty Publications

The antiviral drug Paxlovid has been shown to rapidly reduce viral load. Coupled with vaccination, timely administration of safe and effective antivirals could provide a path towards managing COVID-19 without restrictive non-pharmaceutical measures. Here, we estimate the population-level impacts of expanding treatment with Paxlovid in the US using a multi-scale mathematical model of SARS-CoV-2 transmission that incorporates the within-host viral load dynamics of the Omicron variant. We find that, under a low transmission scenario (Re∼1.2) treating 20% of symptomatic cases would be life and cost saving, leading to an estimated 0.26 (95% CrI: 0.03, 0.59) million hospitalizations averted, 30.61 (95% …

Design, Analysis, And Interpretation Of Treatment Response Heterogeneity In Personalized Nutrition And Obesity Treatment Research, Roger S. Zoh, Bridget H. Esteves, Xiaoxin Yu, Amanda J. Fairchild, Ana I. Vazquez, Andrew G. Chapple, Andrew W. Brown, Brandon George, Derek Gordon, Douglas Landsittel, Gary L. Gadbury, Greg Pavela, Gustavo De Los Campos, Luis M. Mestre, David B. Allison

School of Public Health Faculty Publications

It is increasingly assumed that there is no one-size-fits-all approach to dietary recommendations for the management and treatment of chronic diseases such as obesity. This phenomenon that not all individuals respond uniformly to a given treatment has become an area of research interest given the rise of personalized and precision medicine. To conduct, interpret, and disseminate this research rigorously and with scientific accuracy, however, requires an understanding of treatment response heterogeneity. Here, we define treatment response heterogeneity as it relates to clinical trials, provide statistical guidance for measuring treatment response heterogeneity, and highlight study designs that can quantify treatment response …

Dynamic Influence Diagram-Based Deep Reinforcement Learning Framework And Application For Decision Support For Operators In Control Rooms, Joseph Mietkiewicz, Ammar N. Abbas, Chidera Winifred Amazu, Anders L. Madsen, Gabriele Baldissone

Articles

In today’s complex industrial environment, operators are often faced with challenging situations that require quick and accurate decision-making. The human-machine interface (HMI) can display too much information, leading to information overload and potentially compromising the operator’s ability to respond effectively. To address this challenge, decision support models are needed to assist operators in identifying and responding to potential safety incidents. In this paper, we present an experiment to evaluate the effectiveness of a recommendation system in addressing the challenge of information overload. The case study focuses on a formaldehyde production simulator and examines the performance of an improved Human-Machine Interface …

Approximate Confidence Distribution Computing, Suzanne Thornton, W. Li, M. Xie

Mathematics & Statistics Faculty Works

Approximate confidence distribution computing (ACDC) offers a new take on the rapidly developing field of likelihood-free inference from within a frequentist framework. The appeal of this computational method for statistical inference hinges upon the concept of a confidence distribution, a special type of estimator which is defined with respect to the repeated sampling principle. An ACDC method provides frequentist validation for computational inference in problems with unknown or intractable likelihoods. The main theoretical contribution of this work is the identification of a matching condition necessary for frequentist validity of inference from this method. In addition to providing an example of …

Characteristics And Source-Specific Health Risks Of Ambient Pm2.5-Bound Pahs In An Urban City Of Northern Taiwan, Yu-Chieh Ting, Chun-Hung Ku, Yu-Xuan Zou, Kai-Hsien Chi, Jhy-Charm Soo, Chin-Yu Hsu, Yu-Cheng Chen

Department of Biostatistics, Epidemiology, and Environmental Health Sciences Faculty Publications

Polycyclic aromatic hydrocarbons (PAHs) with highly toxic compounds mainly exist in small-sized particles and can induce considerable human health risks. Studies on PM2.5-bound PAHs and their source-specific human health risks still remain scarce. Daily PM2.5 samples (n = 119) were collected every three days from 2016 to 2017 in Taipei city, Taiwan. Fifteen PAHs in PM2.5 were analyzed via gas chromatography tandem mass spectrometry (GC/MS-MS). We utilized a positive matrix factorization (PMF) model, diagnostic ratios, and potential source contribution function (PSCF) to identify the origins of PM2.5-bound PAHs. The annual concentration of total PAHs (TPAH) was 0.79 ± 0.67 ng …

Sickle Cell Disease Treatment With Arginine Therapy (Start): Study Protocol For A Phase 3 Randomized Controlled Trial., Chris A Rees, David C. Brousseau, Daniel M Cohen, Anthony Villella, Carlton Dampier, Kathleen Brown, Andrew Campbell, Corrie E Chumpitazi, Gladstone Airewele, Todd Chang, Christopher Denton, Angela Ellison, Alexis Thompson, Fahd Ahmad, Nitya Bakshi, Keli D Coleman, Sara Leibovich, Deborah Leake, Dunia Hatabah, Hagar Wilkinson, Michelle Robinson, T Charles Casper, Elliott Vichinsky, Claudia R Morris

Department of Pediatrics Faculty Papers

BACKGROUND: Despite substantial illness burden and healthcare utilization conferred by pain from vaso-occlusive episodes (VOE) in children with sickle cell disease (SCD), disease-modifying therapies to effectively treat SCD-VOE are lacking. The aim of the Sickle Cell Disease Treatment with Arginine Therapy (STArT) Trial is to provide definitive evidence regarding the efficacy of intravenous arginine as a treatment for acute SCD-VOE among children, adolescents, and young adults.

METHODS: STArT is a double-blind, placebo-controlled, randomized, phase 3, multicenter trial of intravenous arginine therapy in 360 children, adolescents, and young adults who present with SCD-VOE. The STArT Trial is being conducted at 10 …

Modeling Biphasic, Non-Sigmoidal Dose-Response Relationships: Comparison Of Brain- Cousens And Cedergreen Models For A Biochemical Dataset, Venkat D. Abbaraju, Tamaraty L. Robinson, Brian P. Weiser

Rowan-Virtua School of Osteopathic Medicine Faculty Scholarship

Biphasic, non-sigmoidal dose-response relationships are frequently observed in biochemistry and pharmacology, but they are not always analyzed with appropriate statistical methods. Here, we examine curve fitting methods for “hormetic” dose-response relationships where low and high doses of an effector produce opposite responses. We provide the full dataset used for modeling, and we provide the code for analyzing the dataset in SAS using two established mathematical models of hormesis, the Brain-Cousens model and the Cedergreen model. We show how to obtain and interpret curve parameters such as the ED50 that arise from modeling, and we discuss how curve parameters might change …

Exploring Experimental Design And Multivariate Analysis Techniques For Evaluating Community Structure Of Bacteria In Microbiome Data, Kelsey Karnik

Department of Statistics: Dissertations, Theses, and Student Work

The gut microbiome plays a crucial role in human health, and by working collaboratively with microbiologists, we aim to further our understanding of the human gut and its impact on human health. Promoting a diverse microbiome is emphasized throughout microbiology literature, and involving a statistician in designing experiments to relate gut bacteria and some measured health outcome is crucial for ensuring valid and accurate results. By adopting new experimental design and analysis methods, researchers can begin to gain a deeper understanding of how the genetics of our food affect the composition of taxa within the gut microbiome. This dissertation is …

Sentiment Analysis Before And During The Covid-19 Pandemic, Emily Musgrove

Mathematics Summer Fellows

This study examines the change in connotative language use before and during the Covid-19 pandemic. By analyzing news articles from several major US newspapers, we found that there is a statistically significant correlation between the sentiment of the text and the publication period. Specifically, we document a large, systematic, and statistically significant decline in the overall sentiment of articles published in major news outlets. While our results do not directly gauge the sentiment of the population, our findings have important implications regarding the social responsibility of journalists and media outlets especially in times of crisis.

Kinetic Particle Simulations Of Plasma Charging At Lunar Craters Under Severe Conditions, David Lund, Xiaoming He, Daoru Frank Han

Mathematics and Statistics Faculty Research & Creative Works

This paper presents fully kinetic particle simulations of plasma charging at lunar craters with the presence of lunar lander modules using the recently developed Parallel Immersed-Finite-Element Particle-in-Cell (PIFE-PIC) code. The computation model explicitly includes the lunar regolith layer on top of the lunar bedrock, taking into account the regolith layer thickness and permittivity as well as the lunar lander module in the simulation domain, resolving a nontrivial surface terrain or lunar lander configuration. Simulations were carried out to study the lunar surface and lunar lander module charging near craters at the lunar terminator region under mean and severe plasma environments. …

Exposure Levels Of Airborne Fungi, Bacteria, And Antibiotic Resistance Genes In Cotton Farms During Cotton Harvesting And Evaluations Of N95 Respirators Against These Bioaerosols, Atin Adhikari, Pratik Banerjee, Taylor Thornton, Daleniece Higgins, Caleb Adeoye, Sonam Sherpa

Department of Biostatistics, Epidemiology, and Environmental Health Sciences Faculty Publications

The USA is the third-leading cotton-producing country worldwide and cotton farming is common in the state of Georgia. Cotton harvest can be a significant contributor to airborne microbial exposures to farmers and nearby rural communities. The use of respirators or masks is one of the viable options for reducing organic dust and bioaerosol exposures among farmers. Unfortunately, the OSHA Respiratory Protection Standard (29 CFR Part 1910.134) does not apply to agricultural workplaces and the filtration efficiency of N95 respirators was never field-tested against airborne microorganisms and antibiotic resistance genes (ARGs) during cotton harvesting. This study addressed these two information gaps. …

Childhood Asthma-Management Practices In Rural Nigeria: Exploring The Knowledge, Attitude, And Practice Of Caregivers In Oyo State, Oyindamola Akinso, Atin Adhikari, Jingjing Yin, Joanne Chopak-Foss, Gulzar H. Shah

Department of Biostatistics, Epidemiology, and Environmental Health Sciences Faculty Publications

Background: Caregivers of asthmatic children have a poor knowledge of proper asthma-management practices in Nigeria. This study examined the knowledge, attitudes, and practice behaviors of caregivers in the management of asthma in children under 5 years of age in Oyo State, Nigeria. Methods: While a mixed method was used in the original research, this brief describes the quantitative method used in this study to evaluate caregivers’ asthma-management practices. A 55-item questionnaire on childhood asthma knowledge, attitude, and practice was administered during child welfare-clinic visits to 118 caregivers. Data were analyzed using the IBM SPSS Version 25.0. Statistical significance was set …

Sex Differences In The Clinical Presentation Of Early Psychosis In A Primary Care Setting, Brooke Carter, Rebecca Rodrigues, Jennifer Reid, Suzanne Archie, Amanda L Terry, Lena Palaniyappan, Arlene G Macdougall, Aristotle Voineskos, Saadia Hameed Jan, Liisa Jaakkimainen, Branson Chen, Neo Sawh, Kelly K. Anderson

Epidemiology and Biostatistics Publications

Primary care is an important part of the help-seeking pathway for young people experiencing early psychosis, but sex differences in clinical presentation in these settings are unexplored. We aimed to identify sex differences in clinical presentation to primary care services in the 1-year period prior to a first diagnosis of psychotic disorder. We identified first-onset cases of non-affective psychotic disorder over a 10-year period (2005-2015) using health administrative data linked with electronic medical records (EMRs) from primary care (n = 465). Detailed information on encounters in the year prior to first diagnosis was abstracted, including psychiatric symptoms, other relevant behaviours, …

Uniqueness For An Inverse Quantum-Dirac Problem With Given Weyl Function, Martin Bohner, Ayça Çetinkaya

Mathematics and Statistics Faculty Research & Creative Works

In this work, we consider a boundary value problem for a q-Dirac equation. We prove orthogonality of the eigenfunctions, realness of the eigenvalues, and we study asymptotic formulas of the eigenfunctions. We show that the eigenfunctions form a complete system, we obtain the expansion formula with respect to the eigenfunctions, and we derive Parseval's equality. We construct the Weyl solution and the Weyl function. We prove a uniqueness theorem for the solution of the inverse problem with respect to the Weyl function.